Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree

Quantum Physics [Submitted on 25 Mar 2026] Efficient Preparation of Graph States using the Quotient-Augmented Strong Split Tree Nicholas Connolly, Shin Nishio, Dan E. Browne, Willian John Munro, Kae Nemoto Graph states are a key resource for measurement-based quantum computation and quantum networking, but state-preparation costs limit their practical use. Graph states related by local complement (LC) operations are equivalent up to single-qubit Clifford gates; one may reduce entangling resources by preparing a favorable LC-equivalent representative. However, exhaustive optimization over the LC orbit is not scalable. We address this problem using the split decomposition and its quotient-augmented strong split tree (QASST). For several families of distance-hereditary (DH) graphs, we use the QASST to characterize LC orbits and identify representatives with reduced controlled-Z count or preparation circuit depth. We also introduce a split-fuse construction for arbitrary DH graph states, achieving linear scaling with respect to entangling gates, time steps, and auxiliary qubits. Beyond the DH setting, we discuss a generalized divide-and-conquer split-fuse strategy and a simple greedy heuristic for generic graphs based on triangle enumeration. Together, these methods outperform direct implementations on sufficiently large graphs, providing a scalable alternative to brute-force optimization. Comments: 18 pages + 4 page appendix, 10 figures, and 3 tables. Comments are welcome Subjects: Quantum Physics (quant-ph); Discrete Mathematics (cs.DM); Combinatorics (math.CO) MSC classes: 05C76(Primary) 05C30, 05C83, 05C90 (Secondary) ACM classes: G.2.1; G.2.2; F.2.1 Cite as: arXiv:2603.23892 [quant-ph]   (or arXiv:2603.23892v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2603.23892 Focus to learn more Submission history From: Nicholas Connolly [view email] [v1] Wed, 25 Mar 2026 03:30:57 UTC (551 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-03 Change to browse by: cs cs.DM math math.CO References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)